Displaying similar documents to “New examples of effective formulas for holomorphically contractible functions”

On Lempert functions in 2 .

Jarnicki, Witold (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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On the restricted Waring problem over 2 n [ t ]

Luis Gallardo (2000)

Acta Arithmetica

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1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, 16 , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is...

Carathéodory balls and norm balls in H p , n = z n : z p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z n : z p < 1 which are balls with respect to the complex l p norm in n are those centered at the origin.

Polynomial cycles in certain local domains

T. Pezda (1994)

Acta Arithmetica

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1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple x , x , . . . , x k - 1 of distinct elements of R is called a cycle of f if f ( x i ) = x i + 1 for i=0,1,...,k-2 and f ( x k - 1 ) = x . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number 7 7 · 2 N , depending only on the degree N of K. In this...

On generalized differential equations in Banach spaces

Tadeusz Poreda

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CONTENTSIntroduction . . . . . . . . 5I. Fundamental problems for generalized differential equations at nonsingular points§1. Introduction . . . . . . . . 6§2. Cauchy problem at nonsingular points for generalized differential equations of the first order . . . . . . . . 6§3. Dependence of solution on parameters and initial conditions . . . . . . . . 8II. Total solutions of generalized linear differential equations§1. Introduction . . . . . . . . 11§2. Form of solutions of generalized...

On a discrete version of the antipodal theorem

Krzysztof Oleszkiewicz (1996)

Fundamenta Mathematicae

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The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping f : S k k there exists a point x S k such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which S k is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of i n f x | | f ( x ) - f ( - x ) | | which were previously known (as far as the author knows) only for f linear (cf. [1]).

Growth of the product j = 1 n ( 1 - x a j )

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of j = 1 n | 1 - x a j | on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when a j is j k or when a j is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when a j is j.    In contrast we show, under fairly general conditions, that the maximum is less than 2 n / n r , where r is an arbitrary positive number. One consequence...

A note on strange nonchaotic attractors

Gerhard Keller (1996)

Fundamenta Mathematicae

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For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ T 1 × + with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties:  1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in T 1 × + . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure.  2. The omega-limit of Lebesgue-a.e point in T 1 × + is Γ ̅ , but for a residual set of points in T 1 × + the omega...